Robust Distributed ℒasso-Model Predictive Control Design: A Case Study on Large-Scale Multi-Robot Systems

Document Type : Research Article

Authors

Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

The complexity and dynamic order of large-scale systems is continuously increasing. Considering the many challenges that exist for these systems, it is very important to provide a robust distributed controller that performs well against uncertainties, computation volume, and interaction between subsystems. A robust-distributed ℒasso-MPC (RD-LMPC) approach is suggested in this study for multi-robot systems in the presence of polytopic uncertainty. In addition, a distributed Kalman filter is used to capture interactions between subsystems. To evaluate and perform the effectiveness of the suggested approach, the results obtained on the multi-robot system are compared with the results of the predictive control methods of the centralized, distributed model, and L1 adaptive control}.

Keywords

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References

[1] T. Gholaminejad, A. Khaki-Sedigh, and P. Bagheri, ”Adaptive Tuning of Model Predictive Control Parameters Based on Analytical Results,” AUT  Journal of Modeling and Simulation, vol. 50, no. 2, pp. 109-116, 2018.
[2] Q. Sun, K. Zhang, and Y. Shi, ”Resilient model predictive control of cyber–physical systems under DoS attacks,” IEEE Transactions on Industrial Informatics, vol. 16, no. 7, pp. 4920-4927, 2019.
 [3] S. Hashemipour, N. Vasegh, and A. Khaki Sedigh, ”Decentralized Model Reference Adaptive Control of Large Scale Interconnected Systems with Both State and Input Delays,” AUT Journal of Modeling and Simulation, vol. 50, no. 1, pp. 3-12, 2018.
 [4] Y. Zhu and E. Fridman, ”Predictor methods for decentralized control of large-scale systems with input delays,” Automatica, vol. 116, p. 108903, 2020.
[5] X.-B. Chen and S. S. Stankovi´c, ”Decomposition and decentralized control of systems with multi-overlapping structure,” Automatica, vol. 41, no. 10, pp. 1765-1772, 2005.
[6] Z. Karami, Q. Shafee, Y. Khayat, M. Yaribeygi, T. Dragiˇcevi´c, and H. Bevrani, ”Decentralized model predictive control of DC microgrids with constant power load,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 1, pp. 451-460, 2019.
 [7] P. Ojaghi, N. Bigdeli, and M. Rahmani, ”An LMI approach to robust model predictive control of nonlinear systems with state-dependent uncertainties,” Journal of Process Control, vol. 47, pp. 1-10, 2016.
[8] C. Liu, H. Li, J. Gao, and D. Xu, ”Robust self-triggered min–max model predictive control for discrete-time nonlinear systems,” Automatica, vol. 89, pp. 333-339, 2018.
[9] P. Ojaghi and M. Rahmani, ”LMI-based robust predictive load frequency control for power systems with communication delays,” IEEE Transactions on Power Systems, vol. 32, no. 5, pp. 4091-4100, 2017.
[10] S. Yu, M. Hirche, Y. Huang, H. Chen, and F. Allg¨ower, ”Model predictive control for autonomous ground vehicles: A review,” Autonomous Intelligent Systems, vol. 1, no. 1, pp. 1-17, 2021.
 [11] D. R. Robinson, R. T. Mar, K. Estabridis, and G. Hewer, ”An efcient algorithm for optimal trajectory generation for heterogeneous multi-agent systems in non-convex environments,” IEEE Robotics and Automation Let ters, vol. 3, no. 2, pp. 1215-1222, 2018.
[12] J. A. Preiss, W. H¨onig, N. Ayanian, and G. S. Sukhatme, ”Downwash- aware trajectory planning for large quadrotor teams,” in 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2017:IEEE, pp. 250-257.
[13] C. E. Luis, M. Vukosavljev, and A. P. Schoellig, ”Online trajectory generation with distributed model predictive control for multi-robot motion planning,” IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 604-611, 2020.
[14] R. A. Shalmani, M. Rahmani, and N. Bigdeli, ”Nash-based robust distributed model predictive control for large-scale systems,” Journal of Process Control, vol. 88, pp. 43-53, 2020.
[15] S. Tang and V. Kumar, ”A complete algorithm for generating safe trajectories for multi-robot teams,” in Robotics Research: Springer, 2018, pp.599-616.
[16] R. Van Parys and G. Pipeleers, ”Distributed model predictive formation control with inter-vehicle collision avoidance,” in 2017 11th Asian Control Conference (ASCC), 2017: IEEE, pp. 2399-2404.
[17] L. Dai, Q. Cao, Y. Xia, and Y. Gao, ”Distributed MPC for formationof multi-agent systems with collision avoidance and obstacle avoidance,”Journal of the Franklin Institute, vol. 354, no. 4, pp. 2068-2085, 2017.
[18] P. Wang and B. Ding, ”A synthesis approach of distributed model predictive control for homogeneous multi-agent system with collision avoidance,” International Journal of Control, vol. 87, no. 1, pp. 52-63, 2014.
[19] G. Xu, T. Long, Z. Wang, and J. Sun, ”Trust-region fltered sequential convex programming for multi-UAV trajectory planning and collision avoid ance,” ISA transactions, vol. 128, pp. 664-676, 2022.
[20] G. K. Larsen, N. D. Van Foreest, and J. M. Scherpen, ”Distributed MPC applied to a network of households with micro-CHP and heat storage,” IEEE Transactions on Smart Grid, vol. 5, no. 4, pp. 2106-2114, 2014.
[21] Z. Feng, G. Wen, and G. Hu, ”Distributed secure coordinated control for multiagent systems under strategic attacks,” IEEE transactions on cyber- netics, vol. 47, no. 5, pp. 1273-1284, 2016.
[22] M. Gallieri, ”Principles of LASSO MPC,” in Lasso-MPC–Predictive Control with L1-Regularised Least Squares: Springer, 2016, pp. 47-63.
[23] J. Zhan, Y. Chen, A. Aleksandrov, and X. Li, ”Robust distributed model predictive control based consensus of general linear multi-agent systems,” in 2019 IEEE International Symposium on Circuits and Systems (ISCAS), 2019: IEEE, pp. 1-5.
[24] H. Li and Y. Shi, ”Distributed model predictive control of constrained non- linear systems with communication delays,” Systems and Control Letters, vol. 62, no. 10, pp. 819-826, 2013.
[25] A. Katriniok, B. Rosarius, and P. M¨ah¨onen, ”Fully distributed model pre- dictive control of connected automated vehicles in intersections: Theory and vehicle experiments,” IEEE Transactions on Intelligent Transportation Systems, 2022.
[26] C. D. Lellis and P. M. Topping, ”Almost-Schur lemma,” Calculus of Variations and Partial Differential Equations, vol. 43, pp. 347-354, 2012.
[27] R. Vadigepalli and F. J. Doyle, ”A distributed state estimation and control algorithm for plantwide processes,” IEEETransactions on Control Systems Technology, vol. 11, pp. 119-127, 2003.
[28] W. Hackbusch, Elliptic differential equations: theory and numerical treat-  ment. Springer, 2017.
[29] W. Alam, N. Ali, H. M. W. Aziz, and J. Iqbal, ”Control of flexible joint robotic manipulator: Design and prototyping,” in 2018 International Con- ference on Electrical Engineering (ICEE), 2018: IEEE, pp. 1-6.
[30] H. Ahmadian, M. Lotf, M. B. Menhaj, H. A. Talebi, and I. Sharif, ”A novel L1 adaptive-hybrid control with guaranteed stability for a class of uncertain nonlinear systems: A case study on SA330 Puma,” Journal of the Franklin Institute, vol. 359, no. 17, pp. 9860-9885, 2022.
AUT Journal of Modeling and Simulation
Volume 55, Issue 1
June 2023
Pages 127-138

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